Problem :
Find the total area between the graphs of f (x) = ex and g(x) = 1 + 2x from x = - 1 to
x = 1.
Note that
ex≥1 + 2x on the interval
[- 1, 0] and
1 + 2x≥ex on the interval
[0, 1]. Therefore the total area between the graphs is
| ex - (1 + 2x)| dx | = | (ex -1 - 2x)dx + (1 + 2x - ex)dx |
|
| = | [ex - x - x2]-10 + [x + x2 - ex]01 |
|
| = | 1 -  + [(2 - e) - 1] |
|
| = |  |
|